Question

Which of the following relations are correct for the cubic crystal:
A. a = b \( \neq \) c
B. a = b = c
C. \( \alpha = \beta = \gamma = 90^\circ \)
D. \( \alpha \neq \beta = \gamma = 90^\circ \)
Choose the correct answer from the options given below:

• A. A and B only
• B. B and C only
• C. B and D only
• D. A and D only

Hint:

Memorize the lattice parameters for the 7 crystal systems. The cubic system is the most symmetric and easiest to remember: all sides are equal, and all angles are 90 degrees.

Answer 1

The Correct Option is B

Step 1: Concept Overview:
This problem requires identifying the defining lattice parameters of a cubic crystal system. Lattice parameters include unit cell edge lengths (a, b, c) and the angles between them (\(\alpha, \beta, \gamma\)).
Step 2: Detailed Analysis:
A cubic crystal system is defined by the following:
1. Equal lattice constants: The lengths of all unit cell edges are equal.
\[ a = b = c \]
Therefore, option B is correct, and option A is incorrect.
2. Right angles: All three interfacial angles are 90 degrees.
\[ \alpha = \beta = \gamma = 90^\circ \]
Therefore, option C is correct, and option D is incorrect.
Step 3: Conclusion:
The defining relationships for a cubic crystal are \(a = b = c\) and \( \alpha = \beta = \gamma = 90^\circ \). Consequently, statements B and C are correct.